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2: Exercise 1.24. There are n married couples arranged at random in a row. 1. Find...
5. If 4 married couples are arranged in a row, find the probability that no husband...
5. If 4 married couples are arranged in a row, find the probability that no husband sits next to his wife. Hint. Let Ak-"kth couple sits together", k = 1.2.3.4. Apply inclusion/exclusion principle and think about the book arrangement on the shelf: P (at least one couple sits together) i-1 i<j<k For instance with i < j. AiAj -"the ith couple and the jth couple go together, the remaining 4 people are arranged in any order".
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a...
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that somebody sits next to his or her spouse? Hint. Label the seats, the individuals, and the couples. There are 6! 720 seating arrangements altogether. Apply inclusion-exclusion to the events A, [ith couple sit next to each other),-1, 2, 3. Count carefully the numbers of arrangements in...
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that so...
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that somebody sits next to his or her spouse? Hint. Label the seats, the individuals, and the couples. There are 6! 720 seating arrangements altogether. Apply inclusion-exclusion to the events Ai = (ith couple sit next to each other2, 3. Count carefully the numbers of arrangements in...
I. At a certain school, 60% of the students wear neither a ring nor a necklace,...
I. At a certain school, 60% of the students wear neither a ring nor a necklace, 20% wear a ring, 30% wear a necklace. Compute the probability that a randomly selected student wears (a) a ring or a necklace; (b) a ring and a necklace 2. A school offers three language classes: Spanish (S), French (F), and German (G). There are 100 students total, of which 28 take S. 26 take F, 16 take G, 12 take both S and...
Suppose n married couples need to cross a river from left to right one by one...
Suppose n married couples need to cross a river from left to right one by one through a narrow bridge. There always must be more men than women on the left side of the river. What is the probability that evrey man will cross after his own wife. The answer is: (N+1)/(2^N) Why?
1) (5pts) Three married couples have purchased theater tickets and are seated in a row consisting...
1) (5pts) Three married couples have purchased theater tickets and are seated in a row consisting of just six seats. a) How many different seating arrangements are possible? TOTAL: b) How many difet seating arangements ave thethrce men (in any order) in the three leftmost seats? TOTAL: c) Assume the theater-goers take their seats in a completely random fashion. Then each of the seating arrangements in part a) are equally likely. Find the probability that the three men end up...
Suppose that the observational units in a study are opposite-sex couples married in CA in 2016....
Suppose that the observational units in a study are opposite-sex couples married in CA in 2016. For each of the following, indicate whether it can legitimately be considered (1) a categorical variable, (2) a quantitative variable, (3) a statistic, or (4) none of the above. Explain each choice briefly. a. The percent of couples in which the woman is older than the man. b. The average age (of the husband and the wife). c. Age difference (between the husband and...
Question 2. Each partner in a sample of 10 married couples was asked how happy each...
Question 2. Each partner in a sample of 10 married couples was asked how happy each is in their own marriage on scale 1 to 100. The ratings by these couples (husband, wife) were: (60,50), (70,65), (80, 81), (80.79), (80,85), (40,35), (50, 55), (60,55), (65,65), (65,60). a) just by looking at the responses without doing any formal calculation, can you arrive at any conclusion about the relationship between the husband and wife responses? Explain your answer. b) Calculate the sample...
The digit 1, 2, ..., n(n > 5) are put at random in a row. (a)...
The digit 1, 2, ..., n(n > 5) are put at random in a row. (a) Show that the probability that the digits 4 and 5 will be adjacent is 2/n. (b) Find the probability that the digits 4 and 5 will not be adjacent. (c) Find the probability that the digits 4 and 5 will be adjacent or the digits 2 and 3 will be adjacent. That is, find P((4 and 5 adjacent) ∪ (2 and 3 adjacent)).
Use a sign test to test each claim. Exercise 3. Children. A researcher interviewed 20 randomly...
Use a sign test to test each claim.
Exercise 3. Children. A researcher interviewed 20 randomly selected newly married couples. Each husband and wife were independently asked the question:"How many children would you like to have?" Their responses are recorded in the table below. At a = 0.05, can you support the claim that couples have a difference of opinion about the number of children they want? 10 2 3 4 2 couple husband 3 wife 1 5 6 7...
5. If 4 married couples are arranged in a row, find the probability that no husband sits next to his wife. Hint. Let Ak-"kth couple sits together", k = 1.2.3.4. Apply inclusion/exclusion principle and think about the book arrangement on the shelf: P (at least one couple sits together) i-1 i<j<k For instance with i < j. AiAj -"the ith couple and the jth couple go together, the remaining 4 people are arranged in any order".
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that somebody sits next to his or her spouse? Hint. Label the seats, the individuals, and the couples. There are 6! 720 seating arrangements altogether. Apply inclusion-exclusion to the events A, [ith couple sit next to each other),-1, 2, 3. Count carefully the numbers of arrangements in...
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that somebody sits next to his or her spouse? Hint. Label the seats, the individuals, and the couples. There are 6! 720 seating arrangements altogether. Apply inclusion-exclusion to the events Ai = (ith couple sit next to each other2, 3. Count carefully the numbers of arrangements in...
I. At a certain school, 60% of the students wear neither a ring nor a necklace, 20% wear a ring, 30% wear a necklace. Compute the probability that a randomly selected student wears (a) a ring or a necklace; (b) a ring and a necklace 2. A school offers three language classes: Spanish (S), French (F), and German (G). There are 100 students total, of which 28 take S. 26 take F, 16 take G, 12 take both S and...
1) (5pts) Three married couples have purchased theater tickets and are seated in a row consisting of just six seats. a) How many different seating arrangements are possible? TOTAL: b) How many difet seating arangements ave thethrce men (in any order) in the three leftmost seats? TOTAL: c) Assume the theater-goers take their seats in a completely random fashion. Then each of the seating arrangements in part a) are equally likely. Find the probability that the three men end up...
Question 2. Each partner in a sample of 10 married couples was asked how happy each is in their own marriage on scale 1 to 100. The ratings by these couples (husband, wife) were: (60,50), (70,65), (80, 81), (80.79), (80,85), (40,35), (50, 55), (60,55), (65,65), (65,60). a) just by looking at the responses without doing any formal calculation, can you arrive at any conclusion about the relationship between the husband and wife responses? Explain your answer. b) Calculate the sample...
Use a sign test to test each claim.
Exercise 3. Children. A researcher interviewed 20 randomly selected newly married couples. Each husband and wife were independently asked the question:"How many children would you like to have?" Their responses are recorded in the table below. At a = 0.05, can you support the claim that couples have a difference of opinion about the number of children they want? 10 2 3 4 2 couple husband 3 wife 1 5 6 7...
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